Finding the molecular volume fraction of an ideal gas

[dg_5021]

A gas has a temperature of 310 K and a pressure of 101 KPa. (a) Find the volume occupied by 1.25 mol of the gas, assuming it is ideal. (b) Assuming the gas molecules can be approximated as small spheres of diameter 2.5x10^-10 meters, determine the fraction of the volume found in part (a) that is occupied by the molecules. (c) In determining the properties of an ideal gas, we assume that molecules are points of zero volume. Discuss the validity of this assumption for the case considered here.

(a) PV=NRT V=(NRT)/P V= ((1.25mol x 8.31 J/molxK x 310 K)/1.01 x10^5Pa)
= 3.19 x 10^-2 m^3

(b)

I was able to do part (a) but I don't know what to do for (b) or (c) or how to start it? Can someone please help? Thanks

 

[ZapperZ]

A gas has a temperature of 310 K and a pressure of 101 KPa. (a) Find the volume occupied by 1.25 mol of the gas, assuming it is ideal. (b) Assuming the gas molecules can be approximated as small spheres of diameter 2.5x10^-10 meters, determine the fraction of the volume found in part (a) that is occupied by the molecules. (c) In determining the properties of an ideal gas, we assume that molecules are points of zero volume. Discuss the validity of this assumption for the case considered here.

(a) PV=NRT V=(NRT)/P V= ((1.25mol x 8.31 J/molxK x 310 K)/1.01 x10^5Pa)
= 3.19 x 10^-2 m^3

(b)

I was able to do part (a) but I don't know what to do for (b) or (c) or how to start it? Can someone please help? Thanks

Figure out what "N" means in PV = NRT. You should know the connection between this, and the total number of molecules in the gas. Once you know this number, then finding the volume occupied by the molecules should be a matter of baby algebra since you should know how to find the volume of a sphere.

For the last part, compare the ratio of the occupied volume with the total volume of the gas. If the Ideal Gas assumption is that the gas molecule's occupied volume is negligible, is the ratio that you obtained is consistent with such an assumption?

Zz.

 

[dg_5021]

(2.5x10^-10)/2 = 1.25x10^-10 m

V= (4 x pie x (1.25x10^-10^3)/3 = 8.18123x10^30 m^3


N= (PV)/(RT) = .000193 Molecules

(3.19 x 10^-2 m^3)/(.000193 Molecules) =165.155 m^3

Did I do part (b) right?

 

[clive]

(2.5x10^-10)/2 = 1.25x10^-10 m

V= (4 x pie x (1.25x10^-10^3)/3 = 8.18123x10^30 m^3


N= (PV)/(RT) = .000193 Molecules

(3.19 x 10^-2 m^3)/(.000193 Molecules) =165.155 m^3

Did I do part (b) right?

$$pV=\nu RT$$
and
$$\nu =\frac{N}{N_A}$$
N-number of molecules
N_A- Avogadro's number

 

[ZapperZ]

(2.5x10^-10)/2 = 1.25x10^-10 m

V= (4 x pie x (1.25x10^-10^3)/3 = 8.18123x10^30 m^3


N= (PV)/(RT) = .000193 Molecules

(3.19 x 10^-2 m^3)/(.000193 Molecules) =165.155 m^3

Did I do part (b) right?

Er... take 12 steps back and look at your "number" here. Does it make sense that you have a FRACTION of a molecule in a gas? You have not understood the meaning of "N" in that equation.

Zz.